Linear systems — Solutions where lines meet

Drag P to where the two lines meet

x + y = 4

x − y = 0

Arrow keys: 0.1 · Shift: 1. Home: initial point · End: intersection. PageUp/Down: change y by one.

One solution

S (2, 2)

The lines intersect at S. Its coordinates satisfy both equations.

P (1, 1)

Equation 1≠ Not satisfied

1 × (1) + 1 × (1)
2 ≠ 4

Equation 2✓ Satisfied

1 × (1) − 1 × (1)
0 = 0

P satisfies only one equation

Model notes

This resource models two linear equations in two real variables; at least one coefficient of x or y in each equation is nonzero.
Integer coefficients and the 0.1 drag grid are input limits, not restrictions on the solution set. Moving P to the intersection uses the exact solution.
Lines extend infinitely; the screen shows only part of them. An intersection outside the view still exists. Use Fit to view to see it.
Solutions and substitutions use exact rational arithmetic. Rounded decimal values are marked with ≈.

Mathematics

Linear systems — Solutions where lines meet

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